GMAT Math : Powers & Roots of Numbers
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #52 : Arithmetic
Which of the following is equal to the following expression?
First, break down the components of the square root:
Combine like terms. Remember, when multiplying exponents, add them together:
Factor out the common factor of 
Factor the 
Combine the factored 
Now, you can pull 
Example Question #2 : Squaring / Square Roots / Radicals
Which of the following expressions is equal to the following expression?
First, break down the component parts of the square root:
Combine like terms in a way that will let you pull some of them out from underneath the square root symbol:
Pull out the terms with even exponents and simplify:
Example Question #32 : Powers & Roots Of Numbers
Which of the following is equal to the twelfth power of the cube root of 
Assume 
The cube root of 
Example Question #32 : Powers & Roots Of Numbers
Which of the following expressions is equal to 
Example Question #32 : Powers & Roots Of Numbers
Assume 
Multiply the eighth power of the fourth root of 
The fourth root of 
The eighth root of 
The product of these expressions is 
Example Question #31 : Understanding Powers And Roots
Which of the following is equal to the eighth root of the square of 
Assume 
The fourth power of 
The fourth root of
The sixteenth power of 
The sixteenth root of 
The sixth root of
The fourth root of
The square of 
This is equivalent to 
Example Question #33 : Powers & Roots Of Numbers
Which of the following numbers has a rational square root and a rational cube root?
Each of the choices is a power of 10, so rewrite each choice as such:
Since 10 itself does not have a rational square root, a necessary and sufficient condition for 
to be rational - is for 
Similarly, for 
Example Question #34 : Powers & Roots Of Numbers
Assume 
Add the tenth power of the fifth root of 
The tenth power of the fifth root of 
The fifth root of 
The tenth power of 
The two expressions are equivalent, so they add up to 
Example Question #34 : Powers & Roots Of Numbers
Which of the following is equivalent to 
This question requires that you understand negative exponents and fractional exponents. To make a negative exponent positive, simply switch its location in the fraction, so this:
becomes:
Then, we need to recognize how to rewrite fractional exponents. In a fractional exponent, the numerator stays as the power to which we are raising our base. The denominator becomes the index of our root. Thus, our fractional exponent becomes:
Four was the denominator of our fractional exponent, so it became the index of our root. In other words, something raised to the power of 
Example Question #31 : Powers & Roots Of Numbers
How can 
To solve this problem, we must remember exponent rules. The powers here need to be added, since the powers are both raising to the same number. The final answer is 
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